What is recorded here?
Friedmann shows that the Einstein equations under a positively curved pressureless cosmological ansatz allow a time-dependent curvature radius, and classifies monotone and expanding-contracting possibilities depending on constants. A universe governed by relativity need not remain static. Friedmann lets the common spatial curvature radius change with time and derives an equation for its evolution under a simplified matter model. Depending on the cosmological constant and initial conditions, the solutions can expand monotonically or expand and contract. This supplies a theoretical possibility to be compared with observation, while leaving the actual universe and several later geometric developments unresolved.
Source-linked catalogue note. A detailed explanatory guide has not yet been prepared for this entry.
Scientific scope
The target is the 1922 positively curved, pressureless matter construction with Einstein equations and a cosmological constant, plus explicit coordinate and metric assumptions. It is not the complete modern FLRW geometry, arbitrary-pressure cosmology, spatially flat models, or the 1924 negative-curvature extension. A later scholarly note flags incomplete geometric precision; the full tensor reduction was not independently certified. Positive spatial curvature does not alone force recollapse: sufficiently large positive cosmological constant permits a monotone branch. Periodic-radius descriptions do not independently prove regular spacetime continuation through zero-radius singularities. The paper does not derive cosmic redshift, fit galaxy recession data, prove our actual universe expands, or determine its age; its numerical period is explicitly illustrative. Lemaître’s later observation connection and Robertson/Walker developments remain separate. Extracted formula glyphs were not visually certified; the normalized first-integral check confirms a narrow root interpretation, not the full proof or singular boundary behavior.
Read the original work
- A. Friedman, Über die Krümmung des Raumes (Zeitschrift für Physik10,377-386,1922), original German scan
- Ellis and Krasiński, Editor’s Note on Friedmann 1922/1924 (General Relativity and Gravitation31,1985-1990,1999), selected scholarly scope commentary
- Instituut-Lorentz, Friedmann papers: institutional manuscript catalogue and work identification
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People and systems
Alexander Friedmann
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English catalogue narrative
Friedmann: a changing radius in positively curved cosmology
Friedmann shows that the Einstein equations under a positively curved pressureless cosmological ansatz allow a time-dependent curvature radius, and classifies monotone and expanding-contracting possibilities depending on constants.
A universe governed by relativity need not remain static. Friedmann lets the common spatial curvature radius change with time and derives an equation for its evolution under a simplified matter model. Depending on the cosmological constant and initial conditions, the solutions can expand monotonically or expand and contract. This supplies a theoretical possibility to be compared with observation, while leaving the actual universe and several later geometric developments unresolved.
Scientific scope
The target is the 1922 positively curved, pressureless matter construction with Einstein equations and a cosmological constant, plus explicit coordinate and metric assumptions. It is not the complete modern FLRW geometry, arbitrary-pressure cosmology, spatially flat models, or the 1924 negative-curvature extension. A later scholarly note flags incomplete geometric precision; the full tensor reduction was not independently certified. Positive spatial curvature does not alone force recollapse: sufficiently large positive cosmological constant permits a monotone branch. Periodic-radius descriptions do not independently prove regular spacetime continuation through zero-radius singularities. The paper does not derive cosmic redshift, fit galaxy recession data, prove our actual universe expands, or determine its age; its numerical period is explicitly illustrative. Lemaître’s later observation connection and Robertson/Walker developments remain separate. Extracted formula glyphs were not visually certified; the normalized first-integral check confirms a narrow root interpretation, not the full proof or singular boundary behavior.
People and systems
Alexander Friedmann
Original sources
- A. Friedman, Über die Krümmung des Raumes (Zeitschrift für Physik10,377-386,1922), original German scan
- Ellis and Krasiński, Editor’s Note on Friedmann 1922/1924 (General Relativity and Gravitation31,1985-1990,1999), selected scholarly scope commentary
- Instituut-Lorentz, Friedmann papers: institutional manuscript catalogue and work identification